Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 748683, 20 pages
http://dx.doi.org/10.1155/2013/748683
Research Article

Asymptotic Behavior of a Viscoelastic Fluid in a Closed Loop Thermosyphon: Physical Derivation, Asymptotic Analysis, and Numerical Experiments

1Grupo de Dinámica No Lineal (DNL), Escuela Técnica Superior de Ingeniería (ICAI), Universidad Pontificia Comillas, 28015 Madrid, Spain
2ICAI, Grupo Interdisciplinar de Sistemas Complejos (GISC) and DNL, Universidad Pontificia Comillas, 28015 Madrid, Spain

Received 11 February 2013; Accepted 19 April 2013

Academic Editor: Douglas Anderson

Copyright © 2013 Justine Yasappan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. C. Cross and H. Greenside, Pattern Formation and Dynamics in Nonequilibrium Systems, Cambridge University Press, New York, NY, USA, 2009.
  2. J. B. Keller, “Periodic oscillations in a model of thermal convection,” Journal of Fluid Mechanics, vol. 26, no. 3, pp. 599–606, 1966. View at Google Scholar · View at MathSciNet
  3. P. Welander, “On the oscillatory instability of a differentially heated fluid loop,” Journal of Fluid Mechanics, vol. 29, no. 1, pp. 17–30, 1967. View at Google Scholar
  4. F. Morrison, Understanding Rheology, Oxford University Press, New York, NY, USA, 2001.
  5. R. Greif, Y. Zvirin, and A. Mertol, “The transient and stability behavior of a natural convection loop,” Journal of Heat Transfer, vol. 107, pp. 684–688, 1987. View at Google Scholar
  6. A. Jiménez Casas and A. Rodríguez-Bernal, Dinámica no Lineal: Modelos de Campo de Fase y un Termosifon Cerrado, Editorial Acadmica Espaola, Lap Lambert Academic Publishing, 2012.
  7. A. Jiménez-Casas and A. Rodríguez-Bernal, “Finite-dimensional asymptotic behavior in a thermosyphon including the Soret effect,” Mathematical Methods in the Applied Sciences, vol. 22, no. 2, pp. 117–137, 1999. View at Google Scholar · View at MathSciNet
  8. A. Jiménez-Casas, “A coupled ODE/PDE system governing a thermosyphon model,” Nonlinear Analysis, vol. 47, pp. 687–692, 2001. View at Google Scholar
  9. J. J. L. Velázquez, “On the dynamics of a closed thermosyphon,” SIAM Journal on Applied Mathematics, vol. 54, no. 6, pp. 1561–1593, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  10. A. Jiménez Casas and A. M. L. Ovejero, “Numerical analysis of a closed-loop thermosyphon including the Soret effect,” Applied Mathematics and Computation, vol. 124, no. 3, pp. 289–318, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  11. A. Rodríguez-Bernal and E. S. van Vleck, “Complex oscillations in a closed thermosyphon,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 8, no. 1, pp. 41–56, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  12. M. A. Herrero and J. J. L. Velázquez, “Stability analysis of a closed thermosyphon,” European Journal of Applied Mathematics, vol. 1, no. 1, pp. 1–23, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  13. A. Liňan, “Analytical description of chaotic oscillations in a toroidal thermosyphon,” in Fluid Physics, M. G. Velarde and C. I. Christov, Eds., Lecture Notes of Summer Schools, pp. 507–523, World Scientific, River Edge, NJ, USA, 1994. View at Google Scholar
  14. A. Rodríguez-Bernal and E. S. Van Vleck, “Diffusion induced chaos in a closed loop thermosyphon,” SIAM Journal on Applied Mathematics, vol. 58, no. 4, pp. 1072–1093, 1998. View at Publisher · View at Google Scholar · View at MathSciNet
  15. D. Henry, Geometric Theory of Semilinear Parabolic Equations, vol. 840 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1981. View at MathSciNet
  16. A. Rodríguez-Bernal, “Attractors and inertial manifolds for the dynamics of a closed thermosyphon,” Journal of Mathematical Analysis and Applications, vol. 193, no. 3, pp. 942–965, 1995. View at Publisher · View at Google Scholar · View at MathSciNet
  17. J. K. Hale, Asymptotic Behavior of Dissipative Systems, AMS, Providence, RI, USA, 1988.
  18. F. P. Incropera, T. L. Bergman, A. S. Lavine, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, 2011.
  19. A. M. Bloch and E. S. Titi, “On the dynamics of rotating elastic beams,” in New Trends in Systems Theory, vol. 7 of Progress in Systems and Control Theory, pp. 128–135, Birkhäauser, Boston, Mass, USA, 1991. View at Google Scholar · View at MathSciNet
  20. A. M. Stuart, “Pertubration theory of infinite-dimensional dynamical systems,” in Theory and Numerics of OrdInary and Partial Differential Equations, M. Ainsworth, J. Levesley, W. A. Light, and M. Marletta, Eds., Oxford University Press, Oxford, UK, 1994. View at Google Scholar
  21. C. Foias, G. R. Sell, and R. Temam, “Inertial manifolds for nonlinear evolutionary equations,” Journal of Differential Equations, vol. 73, no. 2, pp. 309–353, 1988. View at Publisher · View at Google Scholar · View at MathSciNet
  22. A. Rodríguez-Bernal, “Inertial manifolds for dissipative semiflows in Banach spaces,” Applicable Analysis, vol. 37, no. 1-4, pp. 95–141, 1990. View at Publisher · View at Google Scholar · View at MathSciNet
  23. A. M. Fink, Almost Periodic Differential Equations, vol. 377 of Lecture Notes in Mathematics, Springer, Berlin, Germany, 1974. View at MathSciNet
  24. S. Wolfram, The Mathematica book, Cambridge University Press, 1999. View at MathSciNet
  25. Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, 1993. View at MathSciNet
  26. F. Verhulst, Methods and Applications of Singular Perturbations, Springer, New York, NY, USA, 2005. View at Publisher · View at Google Scholar · View at MathSciNet